Martingale selection theorem for a stochastic sequence with relatively open convex values

Details Martingale selection theorem for a stochastic sequence with relatively open convex values Martingale selection theorem for a stochastic sequence with relatively open convex values

2006-02-26

arxiv.org/abs/math/0602587v1

Mathematics

Probability

7 pages

Scientific paper

For a set-valued stochastic sequence $(G_n)_{n=0}^N$ with relatively open convex values $G_n(\omega)$ we give a criterion for the existence of an adapted sequence $(x_n)_{n=0}^N$ of selectors, admitting an equivalent martingale measure. Mentioned criterion is expressed in terms of supports of the regular conditional upper distributions of the elements $G_n$. This result is a refinement of the main result of author's previous paper (Teor. Veroyatnost. i Primen., 2005, 50:3, 480--500), where the sets $G_n(\omega)$ were assumed to be open and where were asked if the openness condition can be relaxed.

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